Field of the Invention
This invention is in the field of telecommunications, in particular in methods to estimate and compensate for impairments in telecommunications data channels.
Description of the Related Art
Prior Art on Characterizing the Channel State of Communication Data Channels
Ever since the advent of the first transatlantic cable back in back in 1858, which to the disappointment of its backers, was only capable of transmitting data at a rate of about 100 words every 16 hours, the impact of imperfect data channels on communications speed and reliability has been apparent to the telecommunications industry.
Making a quick transition to modern times, even modern day electronic wires (e.g. CATV cable), optical fibers, and wireless (radio) methods of data transmission suffer from the effects of imperfect data channels. The data channels are often imperfect because they often contain various signal reflectors that are positioned at various physical locations in the media (e.g. various junctions in a 1D electrical conductor such as wires, or 1D junctions in optical conductors such as optical fiber. For wireless communications, where the media is 3D space, these reflectors can be radio reflectors that are positioned at various locations in space). Regardless of media type and reflector type, reflectors typically distort signal waveforms by creating various echo reflections, frequency shifts, and the like. The net result is that what was originally a clear and easy to interpret signal waveform, sent by a data channel transmitter will, by the time it reaches the receiver, can be degraded by the presence of various echoes and frequency shifted versions of an original signal waveform.
Traditionally, the telecommunications industry has tended to cope with to such problems by using statistical models of these various data channel reflectors and other impairments to create a statistical profile of how the state of a given data channel (channel state) may fluctuate on a statistical basis. Such prior art includes the work of Clarke and Jakes (R. H. Clarke, A statistical theory of mobile-radio reception, Bell Syst. Tech. J., 47, 957-1000 (1968); and W. C. Jakes (ed.), Microwave Mobile Communications, Wiley, New York, 1974)) and indeed such methods are often referred to in the industry as Clarke-Jakes models.
These prior art models were useful, because it helped communications engineers conservatively design equipment that would generally be robust enough for various commercial applications. For example, if the statistical model predicted that waveforms too close together in frequency would tend to be smeared onto each other by channel state with some statistical probability, then the communications specifications could be designed with enough frequency separation between channels to function to some level of statistical probability. Similarly if the statistical model showed that certain statistical fluctuations in channel states would produce corresponding fluctuations in signal intensity, then the power of the transmitted waveforms, or the maximum rate of data transmission, or both could be designed to cope with these statistical fluctuations.
A good review of these various issues is provided by Pahlavan and Levesque, “Wireless Information Networks, Second Edition”, 2005, John Wiley & Sons, Inc., Hoboken N.J. This book provides a good prior art review discussing how wireless radio signals are subject to various effects including multi-path fading, signal-drop off with distance, Doppler shifts, and scattering off of various reflectors.
As a specific example of prior art, consider the challenge of designing equipment for mobile cellular phones (cell phones). When a moving cell phone receives a transmission from non-moving cell phone tower (base station), although some wireless energy from the cell phone tower may travel directly to the cell phone, much of the wireless energy from the cell phone tower transmission will typically reflect off of various reflectors (e.g. the flat side of buildings), and these “replicas” of the original cell phone tower transmission will also be received by the cell phone, subject to various time delays and power loss due to the distance between the cell phone tower, the reflector, and the cell phone.
If the cell phone is moving, reflected “replica” of the original signal will also be Doppler shifted to a varying extent. These Doppler shifts will vary according to the relative velocity and angle between the cell phone tower, the cell phone, and the location of the various buildings (reflectors) that are reflecting the signal.
According to prior art such as the Clarke-Jakes models, statistical assumptions can be made regarding average distributions of the transmitters, receivers, and various reflectors. This statistical model can then, for example be used to help set system parameters and safety margins so that, to a certain level of reliability, the system still function in spite of these effects. Thus prior art allowed reasonably robust and commercially useful systems to be produced.
Polarization Effects:
Certain types of waves, such as light waves and radio waves, can oscillate in various directions or orientations. For example, wireless (radio waves) can be linearly polarized in a single direction, such as horizontal or vertical directions, or they can be circularly polarized so that the direction of the field rotation can vary in a clockwise or counterclockwise manner. For example, wireless antennas often can be configured to transmit linear polarized wireless waveforms.
Often, transmitted light waves and/or radio waves consist of a coherent or incoherent mixture of various types of polarized waves. Generally if there is an equal mix of all polarization types, then the wave is considered to be not polarized. Conversely if one polarization type dominates, the wave is considered to be polarized according to the dominant polarization mode.
Reflectors often do not reflect all polarized waves in exactly the same way. Instead reflectors often absorb some polarization modes, while reflecting other polarization modes. For example, specular reflectors (specular reflection) often only reflects one direction of polarization, which is why polarized sunglasses are often used to cut down on glare. Other types of reflectors, such as such as ground reflection of wireless signals, or reflection off of irregular metal objects, can end up shifting the polarization angle of the reflected waves.
MIMO Techniques
MIMO (multiple-input and multiple-output) radio methods are commonly used for many applications including WiFi and 3G MIMO techniques. The basic principles behind MIMO are described in various US patents such as Roy, 5,515,378, Paulraj, 5,345,599, various papers such as Golden et. al., “Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture” ELECTRONICS LETTERS 35(1) Jan. 7, 1999.
Phased Array Techniques
Phased array antennas are used for a broad range of applications, including RADAR, radio astronomy, AM and FM broadcasting, and the like. On the transmitter side, the basic concept is to operate multiple (e.g. N) transmitters or receivers according to the principles of N-slit diffraction. Thus for transmission, each of the N transmitters will emit the same waveform, each offset by a different phase shift angle. Due to diffraction principles of constructive interference and destructive interference, depending on the phase shift angle, the sum of the resulting waveforms from the N different antennas will impart directionality to the resulting transmitted beam. Similarly, for receiving, the receiver will monitor or detect the phase shifts between the same waveforms as received by N different receiving antennas, thus in effect imparting directionality to the receiver antenna array as well. Patents on phased array methods include Shimko, U.S. Pat. No. 4,931,803, and others.
Review of OTFS Methods
As previously discussed, modern electronics communications, such as optical fiber communications, electronic wire or cable based communications, and wireless communications all operate by modulating signals and sending these signals over their respective optical fiber, wire/cable, or wireless mediums or communications channels. Here these various media are often referred to as “data channels”. In the case of optical fiber and wire/cable, often these data channels comprise a physical medium (e.g. the fiber or cable), often comprising at least one dimension of space and one dimension of time.
In the case of wireless communications, often these data channels will consist of the physical medium of space (and any objects in this space) comprising three dimensions of space and one dimension of time. (Note however, that in the most commonly used commercial setting of ground based wireless applications, often the third spatial dimension of height can be less important, and thus ground based wireless applications can often be adequately approximated as a two dimensional medium of space (with objects) with one dimension of time.)
As previously discussed, as signals travel through a data channel, the various signals (e.g. waveforms), which (at least in the case of optical, wireless, or electric signals) often travel at or near the speed of light, are generally subject to various types of degradation or channel impairments. As per the previous example, echo signals can potentially be generated in an optical fiber or wire/cable medium whenever a signal encounters junctions in the optical fiber or wire/cable. Echo signals can also potentially be generated when wireless signals bounce off of wireless reflecting surfaces, such as the sides of buildings, and other structures. Similarly frequency shifts can occur when the optical fiber or wire/cable propagating signal passes through different regions of fiber or cable with somewhat different signal propagating properties or different ambient temperatures. For wireless signals, signals transmitted to or from a moving reflector, or to or from a moving vehicle are subject to Doppler shifts that also result in frequency shifts. Additionally, the underlying equipment (i.e. transmitters and receivers) do not always operate perfectly, and can produce frequency shifts as well.
These echo effects and frequency shifts are unwanted, and if such shifts become too large, can result in lower rates of signal transmission, as well as higher error rates. Thus methods to reduce such echo effects and frequency shifts are of high utility in the communications field.
In previous work, exemplified by applicant's US patent applications U.S. 61/349,619, U.S. Ser. No. 13/430,690, and Ser. No. 13/927,091 as well as U.S. Pat. Nos. 8,547,988 and 8,879,378, applicant taught a novel method of wireless signal modulation that operated by spreading data symbols over a larger range of times, frequencies, and spectral shapes (waveforms) than was previously employed by prior art methods (e.g. greater than such prior art methods as Time Division Multiple Access (TDMA), Global System for Mobile Communications (GSM), Code Division Multiple Access (CDMA), Frequency Division Multiple Access (FDMA), Orthogonal Frequency-Division Multiplexing (OFDM), or other methods).
Applicant's methods, previously termed “Orthonormal Time-Frequency Shifting and Spectral Shaping (OTFSSS)” in U.S. Ser. No. 13/117,119 (and subsequently referred to by the simpler “OTFS” abbreviation in later patent applications such as U.S. Ser. No. 13/430,690) operated by sending data in larger “chunks” or frames than previous methods. That is, while a prior art CDMA or OFDM method might encode and send units or frames of “N” symbols over a communications link (e.g. data channel) over a set interval of time, applicant's OTFS methods would typically be based on a minimum unit or frame of N2 symbols, and often transmit these N2 symbols over longer periods of time.
In some OTFS modulation embodiments, each data symbol or element that is transmitted was also spread out to a much greater extent in time, frequency, and spectral shape space than was the case for prior art methods. As a result, at the receiver end, it often took longer to start to resolve the value of any given data symbol because this symbol had to be gradually built-up or accumulated as the full frame of N2 symbols is received.
Thus applicant's prior work taught a wireless communication method that used a combination of time, frequency and spectral shaping to transmit data in convolution unit matrices (data frames) of N·N (N2) (e.g. N×N, N times N) symbols. In some embodiments, either all N2 data symbols are received over N spreading time intervals (e.g. N wireless waveform bursts), or none were (e.g. receiving N bursts was required in order to reconstruct the original data bits). In other embodiments this requirement was relaxed.
To determine the times, waveforms, and data symbol distribution for the transmission process, the N2 sized data frame matrix could, for example, be multiplied by a first N·N time-frequency shifting matrix, permuted, and then multiplied by a second N·N spectral shaping matrix, thereby mixing each data symbol across the entire resulting N·N matrix. This resulting data matrix was then selected, modulated, and transmitted, on a one element per time slice basis, as a series of N OTFS symbol waveform bursts. At the receiver, the replica matrix was reconstructed and deconvoluted, revealing a copy of the originally transmitted data.
For example, in some embodiments taught by U.S. patent application Ser. No. 13/117,119, the OTFS waveforms could be transmitted and received on one frame of data ([D]) at a time basis over a communications link, typically using processor and software driven wireless transmitters and receivers. Thus, for example, all of the following steps were usually done automatically using at least one processor.
This first approach used frames of data that would typically comprise a matrix of up to N2 data elements, N being greater than 1. This method was based on creating an orthonormal matrix set comprising a first N×N matrix ([U1]) and a second N×N matrix ([U2]). The communications link and orthonormal matrix set were typically chosen to be capable of transmitting at least N elements from a matrix product of the first N×N matrix ([U1]), a frame of data ([D]), and the second N×N matrix ([U2]) over one time spreading interval (e.g. one burst). Here each time spreading interval could consist of at least N time slices. The method typically operated by forming a first matrix product of the first N×N matrix ([U1]), and the frame of data ([D]), and then permuting the first matrix product by an invertible permutation operation P, resulting in a permuted first matrix product P([1][D]). The method then formed a second matrix product of this permuted first matrix product P([U1][D]) and the second N×N_matrix ([U2]) forming a convoluted data matrix, according to the method, this convoluted data matrix could be transmitted and received over the wireless communications link.
On the transmitter side, for each single time-spreading interval (e.g. burst time), the method operated by selecting N different elements of the convoluted data matrix, and over different time slices in this time spreading interval, the method used a processor and typically software controlled radio transmitters to select one element from the N different elements of the convoluted data matrix, modulate this element, and wirelessly transmit this element so that each element occupied its own time slice.
On the receiver side, the receiver (typically a processor controlled software receiver) would receive these N different elements of the convoluted data matrix over different time slices in the various time spreading intervals (burst times), and demodulate the N different elements of this convoluted data matrix. These steps would be repeated up to a total of N times, thereby reassembling a replica of the convoluted data matrix at the receiver.
The receiver would then use the first N×N matrix ([U1]) and the second N×N matrix ([U2]) to reconstruct the original frame of data ([D]) from the convoluted data matrix. In some embodiments of this method, an arbitrary data element of an arbitrary frame of data ([D]) could not be guaranteed to be reconstructed with full accuracy until the convoluted data matrix had been completely recovered. In practice, the system could also be configured with some redundancy so that it could cope with the loss of at least a few elements from the convoluted data matrix.
U.S. patent application Ser. No. 13/117,119 and its provisional application 61/359,619 also taught an alternative approach of transmitting and receiving at least one frame of data ([D]) over a wireless communications link, where again this frame of data generally comprised a matrix of up to N2 data elements (N being greater than 1). This alternative method worked by convoluting the data elements of the frame of data ([D]) so that the value of each data element, when transmitted, would be spread over a plurality of wireless waveforms, where each individual waveform in this plurality of wireless waveforms would have a characteristic frequency, and each individual waveform in this plurality of wireless waveforms would carry the convoluted results from a plurality of these data elements from the data frame. According to the method, the transmitter automatically transmitted the convoluted results by shifting the frequency of this plurality of wireless waveforms over a plurality of time intervals so that the value of each data element would be transmitted as a plurality of frequency shifted wireless waveforms sent over a plurality of time intervals, again as a series of waveform bursts. At the receiver side, a receiver would receive and use a processor to deconvolute this plurality of frequency shifted wireless waveforms bursts sent over a plurality of times, and thus reconstruct a replica of at least one originally transmitted frame of data ([D]). Here again, in some embodiments, the convolution and deconvolution schemes could be selected so such that an arbitrary data element of an arbitrary frame of data ([D]) could not be guaranteed to be reconstructed with full accuracy until substantially all of the plurality of frequency shifted wireless waveforms had been transmitted and received as a plurality of waveform bursts. (In practice, as before, the system could also be configured with some redundancy so that it could cope with the loss of at least a few cyclically frequency shifted wireless waveforms.) Between frames, the same patterns of time shifts and frequency shifts may repeat, so between frames, these time shifts and frequency shifts can in some embodiments be viewed as being cyclic time sifts and cyclic frequency shifts. Within a given frame, however, although the time shifts and frequency shifts may in some embodiments also be cyclic time shifts and cyclic frequency shifts, this need not always be the case. For example, consider the case where the system is transmitting an M×N frame of data, using M frequencies, over N time periods. Here for each time period, the system may simultaneously transmit M OTFS symbols using M mutually orthogonal carrier frequencies (e.g. tones, subcarriers, narrow band subcarriers, OFDM subcarriers, and the like). The OFTS carrier frequencies (tones, subcarriers) are all mutually orthogonal, and considering the N time periods, are also reused each time period, but otherwise need not be cyclic.
In other embodiments, the methods previously disclosed in U.S. patent application Ser. Nos. 14/583,911, 13/927,091; 13/927/086; 13/927,095; 13/927,089; 13/927,092; 13/927,087; 13/927,088; 13/927,091; and/or provisional application 61/664,020 may be used for some of the OTFS modulation methods disclosed herein. The entire contents of US patent applications 62/027,231, 13/927,091; 13/927/086; 13/927,095; 13/927,089; 13/927,092; 13/927,087; 13/927,088; 13/927,091; 14/583,911, and 61/664,020 are incorporated herein in their entirety.